Grade 8 Polynomial Challenges: Multiply & Factor Fun!

A rectangular garden has a length of (2x + 3) meters and a width of (x + 4) meters. What is the area of the garden as a polynomial?

• 2x^2 + 11x + 10

• 2x^2 + 11x + 12

• 2x^2 + 9x + 12

• 2x^2 + 7x + 12

A box has a volume represented by the polynomial V = (x + 2)(x + 3)(x + 1). If the height of the box is (x + 2), what is the area of the base?

• (x + 3)(x + 2)

• (x + 1)(x + 1)

• (x + 3)(x + 1)

• (x + 2)(x + 2)

The cost of producing x items is given by the polynomial C(x) = 5x^2 + 20x + 15. If the company produces 3 items, what is the total cost?

• 150

• 120

• 90

• 100

A school is planning to build a new playground. The area of the playground is represented by the polynomial A = (x + 5)(x + 2). What is the area in standard form?

• x^2 + 10x + 5

• x^2 + 3x + 15

• x^2 + 7x + 10

• x^2 + 5x + 12

A farmer has a rectangular field with a length of (3x + 1) meters and a width of (2x - 4) meters. What is the polynomial expression for the perimeter of the field?

• 10x - 6

• 10x + 4

• 6x - 8

• 8x - 6

The profit P from selling x items is given by the polynomial P(x) = 10x - (x^2 + 4x). What is the maximum profit when selling 5 items?

• 15

• 0

• 5

• 10

A rectangular pool has a length of (x + 6) meters and a width of (x - 2) meters. What is the polynomial expression for the volume of the pool if the depth is 2 meters?

• 2x^2 + 4x - 12

• 2x^2 - 8x + 16

• 2x^2 + 8x - 24

• 2x^2 + 10x - 20

A company produces a product with a revenue represented by R(x) = (2x + 3)(x + 5). What is the total revenue when x = 4?

• 85

• 120

• 99

• 75

The area of a triangular plot of land is given by the polynomial A = (1/2)(base)(height) = (1/2)(x + 4)(x + 2). What is the area in standard form?

• (1/2)x^2 + 4x + 3

• (1/2)x^2 + 2x + 5

• (1/2)x^2 + 3x + 4

• (1/2)x^2 + 5x + 2

A rectangular box has a length of (x + 1), a width of (x + 2), and a height of (x + 3). What is the polynomial expression for the volume of the box?

• x^3 + 6x^2 + 11x + 6

• x^3 + 5x^2 + 10x + 5

• x^3 + 4x^2 + 9x + 4

• x^3 + 7x^2 + 12x + 8